Explore: Convex Domains

crescent shape, is not convex. The boundary of a convex set in the plane is always a convex curve. The intersection of all the convex sets that contain a

{\displaystyle \mathbb {R} ^{n}} is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an s 0 ∈ S {\displaystyle

41.45. Sin Hitomatsu (1958), "On some conjectures concerning pseudo-convex domains", Journal of the Mathematical Society of Japan, 6 (2): 177–195, doi:10

single variable is convex if and only if its second derivative is nonnegative on its entire domain. Well-known examples of convex functions of a single

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined

true in case of either compact or convex domains. Indeed, a uniformly continuous map f : C → Y defined on a convex set C of a normed space E always admits

function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain elements. Equivalently

correspond to convex domains and pseudoconvex domains, but there are also other types of domains, for instance lineally convex domains which can be generalized

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently

Nitsch; C. Trombetti (2011). "Best constants in Poincaré inequalities for convex domains". arXiv:1110.2960 [math.AP]. Del Pino, M.; Dolbeault, J. (2002). "Best